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Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nystr\"om approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices. [ABSTRACT FROM AUTHOR]

The article introduces a new section structure for the SIAM Journal on Scientific Computing (SISC), including a focus on Scientific Machine Learning as a major development in the field of scientific computing. Topics include the development of accurate, efficient, and scalable machine learning algorithms for solving mathematical modeling problems, emphasizing the importance of reproducibility in the review process.